The error diffusion method is known as an example of pseudo-halftone processing for expressing multivalued data by a binary value (see “An Adaptive Algorithm for Spatial Gray Scale”, Proceedings of the Society for Information Display, 1975, Symposium Digest of Technical Papers, 1975, 36). The error diffusion method, where P represents a pixel of interest, v the density of this pixel, v0, v1, v2 and v3 the densities of pixels P0, P1, P2 and P3, respectively, neighboring the pixel of interest P, and T a threshold value for binarizing these densities, is a method of diffusing binarization error E at the pixel of interest P to the neighboring pixels P0, P1, P2, P3 by weighting coefficients determined empirically, thereby making mean density equal to the density of the original image macroscopically.
According to the error diffusion method, we can write the following with regard to output binary data Do:if v≧T holds, then Do=1, E=v−Vmax;  (1)if v<T holds, then Do=0, E=v−Vmin;
(where Vmax and Vmin represent maximum and minimum density, respectively);v0=v0+E×W0;  (2)v1=v1+E×W1;  (3)v2=v2+E×W2;  (4)v3=v3+E×W3;  (5)
(example of weighting coefficients: W0= 7/16, W1= 1/16, W2= 5/16, W3= 3/16).
Ordinarily, processing is executed while the pixel of interest is shifted in sequence with the raster scan, and often the neighboring pixels P0, P1, P2, P3 chosen are the pixel adjacent the pixel of interest with respect to the scanning direction, the pixel immediately preceding the pixel directly below the pixel of interest, the pixel directly below the pixel of interest and the pixel immediately following the pixel directly below the pixel of interest. Conversely, the pixel of interest receives diffused error from the immediately preceding pixel, the pixel directly above and the two pixels on both sides of the pixel directly above the pixel of interest. Further, there are cases where a pixel neighboring a pixel of interest is non-existent, such as when the pixel of interest is at the beginning or end of a line, or when a line is the first line or last line. As a consequence, a method often adopted in such case is to adopt zero as the weight applied to a non-existent pixel and distribute the binarization error to the other pixels.
Furthermore, if an image to be processed is one of uniform density, there are instances where a visually disagreeable arrangement of printed dots occurs (namely deterioration of visual characteristics). In order to prevent this, the specification of Japanese Patent Application Laid-Open No. 3-88570 discloses a pseudo-halftoning method of selecting optimum weighting coefficients W0, W1, W2, W3 in accordance with density v of the pixel of interest. This method is such that pseudo-halftoning is capable of preventing the visually disagreeable arrangement of printed dots (the deterioration of visual characteristics), which is ascribable to changes in the spatial frequency of the image.
However, a problem arises when pseudo-halftoning is applied to a color image composed of multiple colors, such as the four colors of cyan, magenta, yellow and black employed in color ink-jet printers or the like. Specifically, since each color is processed individually using a method such as the error diffusion method, excellent visual characteristics are obtained when the image of each color is observed but this is not necessarily the case with regard to superimposed images of two or more colors.
In an effort to improve upon this drawback, the specifications of Japanese Patent Application Laid-Open Nos. 8-279920 and 11-10918 disclose a pseudo-halftoning method of obtaining excellent visual characteristics even with regard to superimposed images of two or more colors by combining two or more colors and then applying the error diffusion method.
This error diffusion method applied upon combining two or more colors makes it easy to optimize spatial frequency with regard to the entirety of an image of two or more colors to which error diffusion processing has been applied. However, optimizing the spatial frequency of images on a per-color-component basis is difficult. For example, assume that a color image of two colors has been subjected to this improved error diffusion processing. In this case, the dots will be disposed at a uniform spacing if the two images that have undergone error diffusion processing are observed together. If the image of each color is observed individually, however, dots become connected and unsightly dot placement is the result.